Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants

To probe the microscopic mechanisms that govern the titration behavior of buried ionizable groups, microsecond explicit solvent molecular dynamics simulations are carried out for several mutants of Staphylococcal nuclease using both fixed charge and polarizable force fields. While the ionization of Asp 66, Glu 66, and Lys 125 lead to enhanced structural fluctuations and partial unfolding of adjacent α‐helical regions, the ionization of Lys 25 causes local unfolding of adjacent β sheets. Using the sampled conformational ensembles, good agreement with experimental pK_a values is obtained with Poisson–Boltzmann calculations using a protein dielectric constant of 2–4 for V66D/E; slightly larger dielectric constants are needed for Lys mutants especially L25K, suggesting that structural responses beyond microseconds are involved in ionization of Lys 25. Overall, the set of unbiased simulations provides insights into the spatial and temporal scales of protein and solvent motions that dictate the diverse titration behaviors of buried protein residues. Proteins 2017; 85:268–281. © 2016 Wiley Periodicals, Inc.     

Structure and dynamics of staphylococcal nuclease mutants as studied by fluorescence quenching techniques

Fluorescence techniques have been used to investigate the effect of mutations on the structure and dynamics of staphylococcal nuclease. An estimate of the accessibility to acrylamide of the enzyme's single tryptophan residue (Trp140) was obtained from the Stern-Volmer constant for fluorescence quenching. This was indicative of a partially buried tryptophan in the wild-type nuclease. Five single-site mutant nucleases (H124L, V66L, G88V, G79S and F76V) and one double mutant (V66L + G88V), with widely differing stabilities to denaturants, gave Stern-Volmer constants which were very similar to that of their parent enzyme. Studies of the temperature- and viscosity-dependence of quenching suggest that access by acrylamide to Trp140 is limited by diffusion rather than by protein structural fluctuations. Lifetime-resolved fluorescence anisotropy studies using steady-state instrumentation suggest that there is very little segmental motion of the Trp140; most of the anisotropy therefore decays due to protein rotation in the solution. Rotational correlation times for several nuclease mutants have been determined and these are very similar to that of the native nuclease. Thus it appears that these substitutions in the primary amino acid sequence, which have significant effects on the stability of the folded proteins, do not cause a significant change in the protein structure or dynamics around Trp140.     

Recent development and application of constant pH molecular dynamics

Solution pH is a critical environmental factor for chemical and biological processes. Over the last decade, significant efforts have been made in the development of constant pH molecular dynamics (pHMD) techniques for gaining detailed insights into pH-coupled dynamical phenomena. In this article, we review the advancement of this field in the past five years, placing a special emphasis on the development of the all-atom continuous pHMD technique. We discuss various applications, including the prediction of pK_a shifts for proteins, nucleic acids and surfactant assemblies, elucidation of pH-dependent population shifts, protein–protein and protein–RNA binding, as well as the mechanisms of pH-dependent self-assembly and phase transitions of surfactants and peptides. We also discuss future directions for the further improvement of the pHMD techniques.     

Molecular dynamics study of water penetration in staphylococcal nuclease

The ionization properties of Lys and Glu residues buried in the hydrophobic core of staphylococcal nuclease (SN) suggest that the interior of this protein behaves as a highly polarizable medium with an apparent dielectric constant near 10. This has been rationalized previously in terms of localized conformational relaxation concomitant with the ionization of the internal residue, and with contributions by internal water molecules. Paradoxically, the crystal structure of the SN V66E variant shows internal water molecules and the structure of the V66K variant does not. To assess the structural and dynamical character of interior water molecules in SN, a series of 10-ns-long molecular dynamics (MD) simulations was performed with wild-type SN, and with the V66E and V66K variants with Glu66 and Lys66 in the neutral form. Internal water molecules were identified based on their coordination state and characterized in terms of their residence times, average location, dipole moment fluctuations, hydrogen bonding interactions, and interaction energies. The locations of the water molecules that have residence times of several nanoseconds and display small mean-square displacements agree well with the locations of crystallographically observed water molecules. Additional, relatively disordered water molecules that are not observed crystallographically were found in internal hydrophobic locations. All of the interior water molecules that were analyzed in detail displayed a distribution of interaction energies with higher mean value and narrower width than a bulk water molecule. This underscores the importance of protein dynamics for hydration of the protein interior. Further analysis of the MD trajectories revealed that the fluctuations in the protein structure (especially the loop elements) can strongly influence protein hydration by changing the patterns or strengths of hydrogen bonding interactions between water molecules and the protein. To investigate the dynamical response of the protein to burial of charged groups in the protein interior, MD simulations were performed with Glu66 and Lys66 in the charged state. Overall, the MD simulations suggest that a conformational change rather than internal water molecules is the dominant determinant of the high apparent polarizability of the protein interior.     

Higher-order packing interactions in triple and quadruple mutants of staphylococcal nuclease

Sixty-four triple and 32 quadruple mutants were constructed in the core of staphylococcal nuclease. This is the first time that a large number of multiple mutants with all possible variations and all possible lower-order mutants has been systematically constructed in any protein core. Stabilities were determined by solvent denaturation. The energetic effects of these multiple mutants have been analyzed in combination with the stability data from the component single and double mutants. It was found that most of the stability changes in triple and quadruple mutants cannot be correctly predicted from stability effects of component single mutants. However, if the interaction energy between pairs of side chains in the component double mutants is taken into account, correct stability prediction can be made for most triple and quadruple mutants. The data further show that while packing interactions unique to triple and quadruple mutations do occur, they are of much less energetic significance than interactions between pairs of residues. The results presented here show that the packing of a protein interior can be closely approximated in most cases as a series of short-range, nearest-neighbor interactions. This has profound implications for rational protein design and structure prediction.     

Structural plasticity of staphylococcal nuclease probed by perturbation with pressure and pH

The ionization of internal groups in proteins can trigger conformational change. Despite this being the structural basis of most biological energy transduction, these processes are poorly understood. Small angle X-ray scattering (SAXS) and nuclear magnetic resonance (NMR) spectroscopy experiments at ambient and high hydrostatic pressure were used to examine how the presence and ionization of Lys-66, buried in the hydrophobic core of a stabilized variant of staphylococcal nuclease, affect conformation and dynamics. NMR spectroscopy at atmospheric pressure showed previously that the neutral Lys-66 affects slow conformational fluctuations globally, whereas the effects of the charged form are localized to the region immediately surrounding position 66. Ab initio models from SAXS data suggest that when Lys-66 is charged the protein expands, which is consistent with results from NMR spectroscopy. The application of moderate pressure (<2 kbar) at pH values where Lys-66 is normally neutral at ambient pressure left most of the structure unperturbed but produced significant nonlinear changes in chemical shifts in the helix where Lys-66 is located. Above 2 kbar pressure at these pH values the protein with Lys-66 unfolded cooperatively adopting a relatively compact, albeit random structure according to Kratky analysis of the SAXS data. In contrast, at low pH and high pressure the unfolded state of the variant with Lys-66 is more expanded than that of the reference protein. The combined global and local view of the structural reorganization triggered by ionization of the internal Lys-66 reveals more detectable changes than were previously suggested by NMR spectroscopy at ambient pressure.     

Electrostatic effects in highly charged proteins: salt sensitivity of pKa values of histidines in staphylococcal nuclease

The pK(a) values of most histidines in small peptides and in myoglobin increase on average by 0.30 unit between 0.02 and 1.5 M NaCl [Kao et al. (2000) Biophys. J. 79, 1637]. The DeltapK(a) values reflect primarily the ionic strength dependence of the solvation energy; screening of Coulombic interactions contributes only in a minor way. This implies that Coulombic interactions are weak, or that attractive and repulsive contributions to the pK(a) values are balanced. To distinguish experimentally between these two possibilities, and to further characterize the magnitude and salt sensitivity of surface electrostatic interactions in proteins, the salt dependence of pK(a) values of histidines in staphylococcal nuclease was measured by (1)H NMR spectroscopy. Three of the four histidines titrated with significantly depressed pK(a) values, and the salt sensitivity of all histidine pK(a) values was substantial. In three cases, the pK(a) values increased by a full unit between 0.01 and 1.5 M KCl. Anion-specific effects were found; the pK(a) values measured under equivalent ionic strengths in SCN(-) and SO(4)(2-) were higher than in Cl(-); the order of the sensitivity of pK(a) values to anions was SCN(-) > Cl(-) > SO(4)(2-). Structure-based pK(a) calculations with continuum methods were performed to interpret the measured effects structurally and to test their ability to capture the experimental behavior. Calculations in which the protein interior was treated empirically with a dielectric constant of 20 reproduced the pK(a) values and their dependence on the concentration of Cl(-). According to the calculations, the pK(a) values are depressed because of unfavorable self-energies and repulsive Coulombic interactions. Their striking salt sensitivity reflects screening of weak, repulsive, Coulombic interactions among charges separated by more than 10 A. Long-range Coulombic interactions on the surfaces of proteins are weak, but they can add up to produce substantial electrostatic effects when positive and negative charges are not balanced.     

Fluorescence dynamics of staphylococcal nuclease in aqueous solution and reversed micelles

The dynamical fluorescence properties of the sole tryptophan residue (Trp-140) in Staphylococcus aureus nuclease (EC 3.1.31.1) have been investigated in aqueous solution and reversed micelles composed of either sodium bis(2-ethylhexyl)sulfosuccinate (AOT) in isooctane or cetyltrimethylammonium chloride (CTAC) in isooctane/hexanol (12:1 by volume). The fluorescence decay of nuclease in the different environments can be described by a trimodal distribution of fluorescence lifetimes at approx. 0.5, 1.5 and 5.0 ns. The relative amplitudes depend on the environment. For pH 9.0 solutions the contribution of the two shortest lifetime components in the distribution is largest for AOT and smallest for CTAC reversed micelles. There is reasonable agreement between the average fluorescence lifetime and the fluorescence quantum efficiency confirming a significant fluorescence quenching in AOT reversed micelles. Fluorescence anisotropy decay revealed that the tryptophan environment in aqueous nuclease solutions is rigid on a nanosecond timescale. When nuclease was entrapped into reversed micelles the tryptophan gained some internal flexibility as judged from the distinct presence of a shorter correlation time. The longer correlation time reflected the rotational properties of the protein-micellar system. Modulation of the overall charge of nuclease (isoelectric point pH 9.6) by using buffer of pH 9.0 and pH 10.4, respectively, and of the size of empty micelles by selecting two values of the water to surfactant molar ratio, had only a minor effect on the rotational properties of nuclease in the positively charged reversed micelles. Encapsulation of nuclease in anionic reversed micelles resulted in the development of protein bound to aggregated structures which are immobilised on a nanosecond timescale. According to far UV vircular dichroism results the secondary structure of nuclease only followed the already published pH-dependent changes. Encapsulation had no major effect on the overall secondary structure.     

Predicting the equilibrium protein folding pathway: Structure-based analysis of staphylococcal nuclease

The equilibrium folding pathway of staphylococcal nucleas (SNase) has been approximated using a statistical thermodynamic formalism that utilizes the high-resolution structure of the native state as a template to generate a large ensemble of partially folded states. Close to 400,000 different states ranging from the native to the completely unfolded states were included in the analysis. The probability of each state was estimated using an empirical structural parametrization of the folding energetics. It is shown that this formalism predicts accurately the stability of the protein, the cooperativity of the folding/unfolding transition observed by differential scanning calorimetry (DSC) or urea denaturation and the thermodynamic parameters for unfolding. More importantly, this formalism provides a quantitative account of the experimental hydrogen exchange protection factors measured under native conditions for SNase. These results suggest that the computer-generated distribution of states approximates well the ensemble of conformations existing in solution. Furthermore, this formalism represents the first model capable of quantitatively predicting within a unified framework the probability distribution of states seen under native conditions and its change upon unfolding. © 1997 Wiley-Liss, Inc.     

Constant pH molecular dynamics with proton tautomerism

The current article describes a new two-dimensional lambda-dynamics method to include proton tautomerism in continuous constant pH molecular dynamics (CPHMD) simulations. The two-dimensional lambda-dynamics framework is used to devise a tautomeric state titration model for the CPHMD simulations involving carboxyl and histidine residues. Combined with the GBSW implicit solvent model, the new method is tested on titration simulations of blocked histidine and aspartic acid as well as two benchmark proteins, turkey ovomucoid third domain (OMTKY3) and ribonuclease A (RNase A). A detailed analysis of the errors inherent to the CPHMD methodology as well as those due to the underlying solvation model is given. The average absolute error for the computed pKa values in OMTKY3 is 1.0 pK unit. In RNase A the average absolute errors for the carboxyl and histidine residues are 1.6 and 0.6 pK units, respectively. In contrast to the previous work, the new model predicts the correct sign for all the pKa shifts, but one, in the benchmark proteins. The predictions of the tautomeric states of His12 and His48 and the conformational states of His48 and His119 are in agreement with experiment. Based on the simulations of OMTKY3 and RNase A, the current work has demonstrated the capability of the CPHMD technique in revealing pH-coupled conformational dynamics of protein side chains.     

Magnetic resonance studies of the binding of oligonucleotide substrates to mutants of staphylococcal nuclease

By a combination of NMR docking and model building, the substrate binding site on staphylococcal nuclease was found to accommodate a trinucleotide and to consist of three subsites, each interacting with a single nucleotidyl unit of DNA. Binding of the essential Ca²⁺ activator and substrate cleavage occur between subsites 1 and 2. Hence, catalytically productive binding would span subsites 1 and 2 while nonproductive binding would span subsites 2 and 3. Lys-49 is near subsite 1, and Lys-84 and Tyr-115 interact with substrates at sub site 3 [Weber, D. J., Gittis, A. G., Mullen, G. P., Abeygunawardana, C., Lattman, E. E., Mildvan, A. S. Proteins 13:275–287, 1992]. The proposed locations of these subsites were independently tested by the effects of the K49A, K84A, and Y115A mutations of staphylococcal nuclease on the binding of Mn²⁺, Ca²⁺, and the dinucleotide and trinucleotide substrates, 5′-pdTdA, dTdA, and dTdAdG. These three mutants have previously been shown to be fully active and to have CD and 2D NMR spectra very similar to those of the wild-type enzyme (Chuang, W.-J., Weber, D. J., Gittis, A. G., Mildvan, A. S. Proteins 17:36–48, 1993). All three mutant enzymes and their pdTdA and dTdA complexes (but not their dTdAdG complex) bind Mn²⁺ and Ca²⁺ more weakly than the wild-type enzyme by factors ranging from 2 to 11. The presence of a terminal phosphate as in 5′-pdTdA raises the affinity of the substrate for staphylococcal nuclease and its three mutants by two orders of magnitude and for the corresponding enzyme–metal complexes by three to four orders of magnitude, suggesting that the terminal phosphate is coordinated by the enzyme-bound divalent cation. Such complexation would result in the nonproductive binding of 5′-pdTdA at subsites 2 and 3. Accordingly, the K84A and Y115A mutations significantly weaken the binding of 5′-pdTdA and its metal to staphylococcal nuclease by factors of 2.2 to 37.8, while the K49A mutation has much smaller or no effect. Such nonproductive binding explains the low activity of staphylococcal nuclease with small substrates, especially those With a terminal phosphate. Similarly, the K84A and Y115A mutations weaken the binding of dTdA and its metal complexes to the enzyme by factors of 3.4 to 13.1 while the K49A mutation has smaller effects indicating significant nonproductive binding of dTdA. The trinucleotide dTdAdG binds more tightly to wild-type and mutant staphylococcal nuclease and to its metal complexes than does the dinucleotide dTdA by factors of 2.4 to 12.2, reflecting the occupancy of an additional subsite. Predominantly productive binding of dTdAdG is indicated by the 1.7? to 8.3?fold lower affinities of the K49A, K84A, and Y115A mutants for the trinucleotide and its metal complexes. The largest effects on dTdAdG binding are seen with the Y115A mutation presumably reflecting the dual role of Tyr-115 both in donating a hydrogen bond to a phosphodiester oxygen between subsites 2 and 3 and in stacking onto the guanine base at subsite 3. © 1994 John Wiley & Sons, Inc.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Fluctuations and correlations in crystalline protein dynamics: a simulation analysis of staphylococcal nuclease

Understanding collective motions in protein crystals is likely to furnish insight into functional protein dynamics and will improve models for refinement against diffraction data. Here, four 10 ns molecular dynamics simulations of crystalline Staphylococcal nuclease are reported and analyzed in terms of fluctuations and correlations in atomic motion. The simulation-derived fluctuations strongly correlate with, but are slightly higher than, the values derived from the experimental B-factors. Approximately 70% of the atomic fluctuations are due to internal protein motion. For 65% of the protein atoms the internal fluctuations converge on the nanosecond timescale. Convergence is much slower for the elements of the interatomic displacement correlation matrix--of these, >80% converge within 1 ns for interatomic distances less, approximately <6 A, but only 10% for separations approximately =12 A. Those collective motions that converged on the nanosecond timescale involve mostly correlations within the beta-barrel or between alpha-helices of the protein. The R-factor with the experimental x-ray diffuse scattering for the crystal, which is determined by the displacement variance-covariance matrix, decreases to 8% after 10 ns simulation. Both the number of converged correlation matrix elements and the R-factor depend logarithmically on time, consistent with a model in which the number of energy minima sampled depends exponentially on the maximum energy barrier crossed. The logarithmic dependence is also extrapolated to predict a convergence time for the whole variance-covariance matrix of approximately 1 micros.     

Coupling between local structure and global stability of a protein: mutants of staphylococcal nuclease

Staphylococcal nuclease exists in solution as a mixture of two folded (N and N') and two unfolded (U and U*) forms. Earlier workers [Evans et al. (1989) Biochemistry 28, 362] have proposed that the N'/N and U/U* structural differences involve cis/trans isomerization about the Lys116-Pro117 peptide bond with N and U cis and N' and U* trans. The present results show that residue changes throughout the nuclease structure have large effects on the distribution of the N and N'forms. The N'/N ratios at 313 K for nuclease H124L (N'/N = 0.07) and nuclease G79S (N'/N = 12) differ by 2 orders of magnitude. Thermodynamic parameters for equilibria linking the two folded and two unfolded substates were evaluated for seven mutants of nuclease which were found by kinetic assays to have similar enzymatic activities but by NMR spectroscopy to have a wide dispersion of thermal stabilities. Our results indicate that mutational perturbations of the N'/N equilibrium in folded nuclease (delta G for the N in equilibrium N' reaction) are strongly coupled to changes in the stability of the N form (delta G for the N in equilibrium U reaction), but much less so to the stability of the N' form (delta G for the N' in equilibrium U* reaction).     

Electron spin echo modulation and nuclear relaxation studies of staphylococcal nuclease and its metal-coordinating mutants

Electron spin echo envelope modulation (ESEEM) spectroscopy has been applied to the determination of the number of water molecules coordinated to the metal in the binary complex of staphylococcal nuclease with Mn2+, to the ternary enzyme-Mn2+-3',5'-pdTp complex, and to ternary complexes of a number of mutant enzymes in which metal-binding ligands have been individually altered. Quantitation of coordinated water is based on ESEEM spectral comparisons of Mn2+-EDTA and Mn2+-DTPA, which differ by a single inner sphere water, and with Mn2+-(H2O)6. It was found that Mn2+ in the ternary complex of the wild-type enzyme has a single additional coordinated water, as compared to Mn2+ in the binary complex, confirming earlier findings based on T1 measurements of bound water [Serpersu, E. H., Shortle, D. L., & Mildvan, A. S. (1987) Biochemistry 26, 1289-1300]. Ternary complexes of the mutant proteins D40E, D40G, and D21Y have the same number of water ligands as the ternary complex of the wild-type enzyme, while the D21E mutant has one less water ligand. In order to maintain octahedral coordination geometry, these findings require two additional ligands to Mn2+ from the protein in the binary complex of the wild-type enzyme, probably Glu 43 and Asp 19, and one additional ligand from the protein in the ternary D40G and D21E complexes. Other ESEEM studies of ternary Mn2+ complexes of wild-type, D21E, and D21Y mutants indicate the coordination by Mn2+ of a phosphate of 3',5'-pdTp, as demonstrated by a 31P contact interaction of 3.9 +/- 0.3 MHz. Magnetic interaction of Mn2+ with 31P could not be demonstrated with the D40G and D40E mutants, suggesting that metal-phosphate distances are greater in these mutants than in the wild-type protein. In a parallel NMR study of the paramagnetic effects of enzyme-bound Co2+ (which occupies the Mn2+ site on the enzyme) on the T1 of 31P from enzyme-bound 3',5'-pdTp and 5'-TMP, it was found that metal to 5'-phosphate distances are 0.9-1.6 A shorter in ternary complexes of the wild-type enzyme and of the D21E mutant than in ternary complexes of the D40G mutant. In all cases, the 5'-phosphate of pdTp is in the inner coordination sphere of Co2+ and the 3'-phosphate is predominantly in the second coordination sphere.     

Stability mutants of staphylococcal nuclease: large compensating enthalpy-entropy changes for the reversible denaturation reaction

By use of intrinsic fluorescence to determine the apparent equilibrium constant Kapp as a function of temperature, the midpoint temperature Tm and apparent enthalpy change delta Happ on reversible thermal denaturation have been determined over a range of pH values for wild-type staphylococcal nuclease and six mutant forms. For wild-type nuclease at pH 7.0, a Tm of 53.3 +/- 0.2 degrees C and a delta Happ of 86.8 +/- 1.4 kcal/mol were obtained, in reasonable agreement with values determined calorimetrically, 52.8 degrees C and 96 +/- 2 kcal/mol. The heat capacity change on denaturation delta Cp was estimated at 1.8 kcal/(mol K) versus the calorimetric value of 2.2 kcal/(mol K). When values of delta Happ and delta Sapp for a series of mutant nucleases that exhibit markedly altered denaturation behavior with guanidine hydrochloride and urea were compared at the same temperature, compensating changes in enthalpy and entropy were observed that greatly reduce the overall effect of the mutations on the free energy of denaturation. In addition, a correlation was found between the estimated delta Cp for the mutant proteins and the d(delta Gapp)/dC for guanidine hydrochloride denaturation. It is proposed that both the enthalpy/entropy compensation and this correlation between two seemingly unrelated denaturation parameters are consequences of large changes in the solvation of the denatured state that result from the mutant amino acid substitutions.     

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.     

Measuring the successes and deficiencies of constant pH molecular dynamics: a blind prediction study

A constant pH molecular dynamics method has been used in the blind prediction of pK(a) values of titratable residues in wild type and mutated structures of the Staphylococcal nuclease (SNase) protein. The predicted values have been subsequently compared to experimental values provided by the laboratory of García-Moreno. CpHMD performs well in predicting the pK(a) of solvent-exposed residues. For residues in the protein interior, the CpHMD method encounters some difficulties in reaching convergence and predicting the pK(a) values for residues having strong interactions with neighboring residues. These results show the need to accurately and sufficiently sample conformational space in order to obtain pK(a) values consistent with experimental results.